Variable-coefficient F-expansion method and its application to nonlinear Schrödinger equation

A Direct Transformation Method and its Application to Variable Coefficient Nonlinear Equations of Schrödinger Type

“…Considering the dark soliton solution u B.5 of (1), we can see that it describes the chirped dark soliton pulse for (1) 2 , and c 4 = a 4 2 , then the solutions ψ 13 , ψ 13 , ψ 22 , ψ 22 , ψ 33 , and ψ 33 in [4] are exactly the same as those obtained in this paper, named u A.1.1 , u B.5 , u A.4 , u B.6 , u A.8 , and u C.3 , respectively. In fact, the exact solutions u A.1.1 to u A.10 of (1), which are expressed by the single Jacobi elliptic function, can all be obtained in [4] with the above condition and in [16] …”

“…Soliton solutions and the Backlund transformation for (1) have been studied in [2] and multisoliton solutions in terms of double Wronskian determinant for (1) have been derived in [3]. Families of exact solutions of (1) have been obtained in [4] by the variable coefficient Fexpansion method. Generation, compression and propagation of pulse trains of (1) have been discussed in [14].…”

“…4 , λ = a 2 , and µ = −4a 4 . Comparing our work with the results in [4] and [16], we present more Jacobi doubly periodic solutions and soliton solutions and our computation is much simpler.…”

Exact and explicit solutions to the discrete nonlinear Schrödinger equation with a saturable nonlinearity

“…Nowadays, some modern analytic methods are available for analyzing nonlinear evolution-type equations. For instance, tanh function method [20], homotopy perturbation method [21], variational iteration method [22], first integral method [23], Expfunction method [24], multiple Exp-function method [25], linear superposition principle [26], Wronskian technique [27], the Fexpansion method [28], the Jacobi elliptic-function method [29], the similarity transformation method [30], the ansätze method [31]. On the other hand, since it was first enunciated in 2008 by 0375-9601/$ -see front matter © 2011 Elsevier B.V. All rights reserved.…”

Non-TravellingWave Solutions of the (2+1)-Dimensional Dispersive Long Wave System

“…There are many powerful and direct methods to construct the exact solutions of NLPDEs, such as the inverse scattering transform [1], tanh-function method [2 -4], the generalized hyperbolic function method [5,6], Exp-function method [7], sine/cosine method [8] and so on. Recently, many exact solutions expressed by Jacobi elliptic functions (JEFs) of NLEEs have been obtained by Jacobi elliptic function expansion method [9 -11], mapping method [12,13], F-expansion method [14], the extended F-expansion method [15], the improved generalized F-expansion method [16,17], the generalized Jacobi elliptic function method [18,19], the variable-coefficient F-expansion method [20] and other methods [21 -23]. The F-expansion method [14] is an over-all generalization of Jacobi elliptic function expansion method.…”